Experimental analysis and safety assessment of thermal runaway behavior in lithium iron phosphate batteries under mechanical abuse

Mechanical abuse can lead to internal short circuits and thermal runaway in lithium-ion batteries, causing severe harm. Therefore, this paper systematically investigates the thermal runaway behavior and safety assessment of lithium iron phosphate (LFP) batteries under mechanical abuse through experimental research. Mechanical abuse experiments are conducted under different conditions and battery state of charge (SOC), capturing force, voltage, and temperature responses during failure. Subsequently, characteristic parameters of thermal runaway behavior are extracted. Further, mechanical abuse conditions are quantified, and the relationship between experimental conditions and battery characteristic parameters is analyzed. Finally, regression models for battery safety boundaries and the degree of thermal runaway risk are established. The research results indicate that the extracted characteristic parameters effectively reflect internal short circuit (ISC) and thermal runaway behaviors, and the regression models provide a robust description of the battery's safety boundaries and thermal runaway risk degree. This work sheds light on understanding thermal runaway behavior and safety assessment methods for lithium-ion cells under mechanical abuse.


A/B
The coefficients of the stress-strain curve Cp i The specific heat capacity of material I (J/(kg K)) d factor The diameter factor of the punch d(x, y, z) The overall diameter curvature at a point in space (x,y,z) dT max The maximum temperature rate (°C/s) dV The voltage drop rate (mV/s) dV (t) dt The voltage rate with respect to experiment time t (mV/s) E F G Coefficients of the first fundamental forms coefficients of surface patch F cr The critical force of mechanical response (kN) F safe The force safety boundary F(t) The force with respect to experiment time t (kN) H The mean curvature H factor The average curvature factor of punch H(x, y, z) The mean curvature at a point in space (x,y,z) The ISC current with respect to experiment time t (A) L M N Coefficients of the second fundamental forms coefficients of surface patch M i The mass of material I (kg) n The hardening index of the stress-strain curve Q isc The heat generation from ISC (J) Q side The heat generation from side reactions (J) R 2 adjusted The adjusted coefficient of determination r isc (t) The ISC resistance with respect to experiment time t (Ω) Severty The thermal runaway risk degree T bt T bl Temperature of the top/low of the back of the battery (°C) T ft T fl The temperature of the top/low of the front of the battery (°C) T i The average temperature at 200 s of material i (°C) T i_0 The initial temperature of material i (°C) T i (t)/T j (t) The temperature at measuring point i/j (°C) T max The maximum temperature (°C) T neg T pos Battery negative/positive temperature (°C) t end The moment the voltage drops to 1 V (s) t isc The start moment of the ISC (s) V end The voltage of the battery with respect to experiment time t end (V) V isc .
The voltage of the battery with respect to experiment time t isc (V) V (t) The voltage with respect to experiment time t (V) x cr The critical displacement of mechanical response (mm) x safe The displacement safety boundary x t The displacement with respect to experiment time t (mm)

Greek symbols α x
The correction coefficients of the displacement safety boundary α F The correction coefficients of the force safety boundary ε p The plastic strain σ 1 σ 2 σ 3 The principal stresses (MPa) σ e The von Mises failure criteria (MPa) σ p The plastic stress (MPa) H The enthalpy change (J) In the face of the dual challenges of the global energy crisis and environmental protection, developing new energy vehicles to replace traditional fossil fuel vehicles has gradually become a global consensus and trend 1 .As a core component of new energy vehicles, lithium-ion batteries have also experienced rapid development in recent years, and researchers carried out a large and systematic work from battery models [2][3][4] , battery thermal management systems (BTMS) [5][6][7] , and battery safety management [8][9][10] .However, ISC and thermal runaway caused by mechanical damage are still tricky and have constrained their development and application.Reports and statistics on fire/ explosion incidents indicate that collisions are the leading cause of such incidents 11 .
Upon mechanical abuse such as collision, squeezing, and puncturing, batteries undergo deformation, damaging and rupturing internal components (separator, electrodes).The contact between the positive and negative electrodes causes ISC, generating a substantial amount of heat, subsequently resulting in thermal runaway, accompanied by phenomena such as leakage, smoke, and combustion [12][13][14] .Researchers have conducted extensive experiments, theoretical studies, and simulations in response to this issue.In terms of mechanical abuse experiments, researchers have explored experiments under quasi-static squeezing 15,16 , dynamic loads 17,18 , different shapes of punch 19,20 , different battery types [21][22][23] , and different battery SOC 17 .These experiments aim to capture changes in parameters such as voltage, force, and temperature during the battery's failure process.Techniques like electrochemical impedance spectroscopy (EIS) 24 , relaxation time distribution (DRT) 25 , and

32Ah LFP battery
This paper uses a 32 Ah lithium iron phosphate square aluminum case battery as a research object.Table 1 shows the relevant specifications of the 32Ah LFP battery.The electrolyte is composed of a standard commercial electrolyte composition (LiPF 6 dissolved in ethylene carbonate (EC):dimethyl carbonate (DMC):methyl ethyl carbonate (EMC): 2:3:5 in volume).Supplementary Fig. S1 online shows the three-dimensional battery geometry and computed tomography (CT) graphics containing two jell rolls.

The experimental settings
A battery has been cycled three times, and the average value of three discharging capacity determines its capacity.A cycled procedure includes a "CC-CV" charge procedure, two rested procedures, and a CC discharge procedure.Supplementary Fig. S2 online presents the cycled procedure and CC-CV charging curves of the 32 Ah LFP Li-ion cell.To maintain the consistency of the batteries, batteries whose capacity deviates from the rated capacity by more than 5%.
Twenty batteries with no more than 5% consistency were selected and divided into five groups for the mechanical abuse experiment.Each battery group was adjusted to a different capacity(100%SOC, 80%SOC, 60%SOC, and 20%SOC).
Five punches with different shapes and sizes were designed to simulate different mechanical abuse scenarios, as shown in Fig. 1.The punch sizes ranged up to 84% of the cell surface area, and the shapes included spherical, The schematic diagram of the test platform is depicted in Fig. 1.An RJD-ZJ pack nail penetration and crush tester with a maximum range of 200 kN, sourced from Shenzhen Ruijiada Technology Co., Ltd., was utilized to record displacement and pressure data during the experiments.A digital camera was employed to capture the dynamic changes in battery behavior during the experiments.A Ti401P infrared thermal imager, sourced from Fluke Corporation, was utilized to capture the thermal image of the battery.Seven K-type thermocouples, designated as T pos -T s in Fig. 1, were affixed to the battery surface to record temperature data with an accuracy of ± 1°C and were connected to a data logger.The GL980 data acquisition instrument (DAQ), sourced from GRAPHTTEC Corporation, was used to collect battery temperature and voltage data at intervals of 100 ms.Before testing, seven thermocouples were fixed on the surface of the Li-ion cell, connecting voltage acquisition, and then the cell was placed in the tester.The test speed was set at 30 mm/min.Maintain test environment at constant ambient temperature (25 ± 2 °C).During the test, the voltage, temperature, force, and displacement data are recorded in real time, a digital video camera captures images of the whole process, and a thermal imager records the temperature distribution of the battery after the thermal runaway.
To minimize experimental uncertainties, all instruments used in the experiments were calibrated before the start of the experiments and operated strictly according to the manufacturer's recommendations.Environmental conditions were maintained constant during the experiments, batteries were randomly assigned to experimental and control groups, and all factors that could affect the experimental results were recorded and controlled.This rigorous approach aimed to maximize the reduction of experimental errors.Additionally, three sets of repeat experiments ensured reproducibility before formal testing.

Results and discussions
In the case of a 60% SOC battery and a 30 mm hemispherical punch condition, Fig. 2 illustrates the mechanical-electrical-thermal response of the battery throughout the mechanical abuse process.The experimental process can be divided into four stages based on the changes in battery voltage, temperature, deformation, and force.
Stage I: Battery deformation stage.The battery gradually deforms as the punch intrudes, and the casing remains intact.At this stage, the force on the battery gradually increases with time/intrusion distance, and the voltage and temperature show no significant changes.
Stage II: Initiation of ISC.The battery voltage decreases with a voltage change rate dV (t) dt > 10mV s .ISC phenomena appear, emitting much white smoke, as shown in Fig. 2b.The force rises, while the temperature shows no significant change.Stage II is relatively short, lasting only 3.5 s in Fig. 2a.
Stage III: Thermal runaway stage.At this point, the force peaks, the battery casing ruptures, and the battery materials are damaged, causing a rapid force drop.As the punch intrudes into the battery, widespread ISC occurs, and the battery voltage rapidly drops to 0 V while the temperature rises rapidly, leading to thermal runaway.
Stage IV: Battery cooling stage.As the thermal runaway ends, the battery begins to cool slowly.In this case, except for the compressed and damaged areas, the battery still maintains a relatively intact appearance, but its internal materials undergo significant carbonization due to the thermal runaway reaction.

Mechanical response and characteristic parameter extraction
Supplementary Fig. S3 online shows the force-displacement data collected by the extrusion machine.The overall force-displacement curves for the battery are similar, with low stiffness in the early stage and a relatively smooth curve.In the later stage, the stiffness increases as the stacked electrodes in the battery gradually compact.Comparing the experimental results for different SOC batteries in each group, the force of different SOC batteries is similar, and the peak force and corresponding displacement are also similar.Therefore, the mechanical response of the LF32 battery is relatively independent of the battery SOC. Figure 3a takes 60% SOC batteries from each group, showing varied maximum force under different conditions, ranging from 3kN for the conical condition to 190kN for the cylindrical flat condition.Generally, the larger the force-bearing area of the battery, the greater the force it can withstand.The maximum force corresponds to different intrusion displacements, ranging from 3.59 mm for the conical condition to 8.63 mm for the 60 mm spherical punch condition.In general, battery failure can be explained from the perspective of material failure criteria.The battery separator material fails when subjected to particular stress or strain.A higher force is needed for a battery with a larger force-bearing area to achieve the same stress.
To further compare the mechanical response of the LF32 battery, Eqs. ( 1) and ( 2) were used to extract the critical force F cr and the corresponding critical displacement x cr under different conditions, as shown in Fig. 4a.These two features reflect the critical state the battery can withstand before the casing breaks.Figure 4a shows that as the contact area between the punch and the battery increases, from conical to hemispherical to flat, the force the battery can withstand increases gradually.The overall trend of critical displacement for the battery is similar to critical force, only closer in numerical range.The maximum and minimum force difference is nearly 60 times, while the maximum and minimum displacement differs by less than 2.3 times.

Electrical response and characteristic parameter extraction
Comparing the experimental results for different SOC batteries in each group, the voltage decreases when Stage II starts, reaching below 1 V within about 20 s (Supplementary Fig. S4 online).The voltage-time curves for the battery are generally similar, and the electrical response of the LF32 battery is relatively independent of battery SOC. Figure 3b takes 60% SOC batteries from each group as an example, showing a similar overall decreasing trend.The moment of the ISC increases with the force-bearing area of the battery.The moment of the ISC is the smallest for the conical condition and largest for the plate condition.The voltage drop rate among different groups decreases with the force-bearing area of the battery.From the perspective of force, the larger the force-bearing area, the larger the area under force, and thus, the greater the force the battery can withstand.Therefore, when ISC occurs with a larger force-bearing area, the triggered failure area for ISC is more significant, resulting in a minor ISC resistance and a faster voltage drop rate for the battery.
Characteristic parameters of the electrical response under mechanical abuse were extracted: the moment of ISC and the voltage drop rate.The starting moment of the ISC t isc was determined when the voltage change rate reached dV (t) dt > 10mV s , as shown in the Eq. (3).Comparing the voltage drop curves, 1 V was chosen as the end time t end to comprehensively reflect the voltage drop rate.The Eq. ( 5) represents the voltage drop rate, reflecting the size of the internal failure area of the battery, with a more significant rate indicating a larger ISC failure area. (1)

Thermal response and characteristic parameter extraction
The experiment equipped the battery surface with seven temperature sampling points.When the battery triggers ISC and enters Stage III, as the punch intrudes and thermal runaway occurs, the ISC area gradually extends from the front center point outward, eventually expanding to the entire battery (Supplementary Fig. S5 online).
The heat generated by ISC and thermal runaway takes time to conduct within the battery, so the temperatures of T ft and T fl closest to the ISC area rise first, while the temperatures of the farthest battery terminals Tneg and Tpos rise more slowly.The battery's maximum temperature difference (MTD) is calculated according to the Eq. ( 6).The MTD quickly rises after the battery triggers ISC due to the rapid response of T f1 and T ft .As thermal runaway extends to the entire battery, MTD begins to decrease, and after 200 s, the temperature difference drops to 36 °C.To highlight the temperature response of the battery during ISC thermal runaway, T ft , representing the temperature with a faster response, was selected for further analysis.
Comparing the experimental results for different SOC batteries in each group, when Stage III starts, and the battery experiences ISC and thermal runaway, the temperature rapidly rises as thermal runaway extends from the central region to the entire battery (Supplementary Fig. S6 online).The temperature-time curves for the battery are generally similar, with high SOC batteries having higher energy, resulting in higher peak temperatures after the thermal runaway.Figure 3c takes 60% SOC batteries from each group as an example, showing that the highest temperature reached by the battery has no apparent correlation with the battery contact area.
Characteristic parameters of the thermal response under mechanical abuse were extracted: the maximum temperature of the battery and the maximum temperature rise rate, as shown in Eqs.(7) and (8).The maximum temperature of the battery is positively correlated with the enthalpy change 40 , usually representing the energy released by the battery during thermal runaway.Typically, 1 °C/s is a critical reference indicator for thermal runaway triggering.The larger the maximum temperature rise rate, the more intense the reaction during thermal runaway.
Figure 4c plot T max and dT max for the battery.Comparing the results T max within the same group, the battery has less energy as SOC decreases, resulting in a minor enthalpy change corresponding to thermal runaway and, thus, a more minor T max .Between different groups, there is no apparent pattern for T max .The pattern for dT max is generally similar to T max .Within the same group, dT max generally decreases with smaller SOC, while there is no clear pattern between different groups.

Quantitative analysis of abuse conditions
This study starts by quantitatively analyzing the mechanical abuse conditions, considering variations in the punch's shape and the battery's SOC.Previous analyses indicate a correlation between the mechanical-electricalthermal response of the battery and the compressed area of the battery.As the punch initially contacts the battery, the sharper the punch, the smaller the contact area (e.g., group 1).As the compression progresses, the overall diameter of the punch decreases, resulting in a smaller contact area (e.g., group 2).Therefore, this paper defines H factor and d factor to describe the sharpness of the punch and its overall diameter, respectively.
To describe the sharpness of the punch, consider the mean curvature H, as shown in Eq. ( 9) 43 .Since the maximum mean curvature values in the five experiments are not in the same order of magnitude, take the logarithm of the maximum mean curvature as the descriptive quantity, as shown in the Eq.(10).The logarithmic distribution of the maximum mean curvature for the five experiments is illustrated in Fig. 5.
where E , F , G are coefficients of the first fundamental forms coefficients of surface patch, and L , M , N are coef- ficients of the second fundamental forms coefficients of surface patch.
The overall diameter of the battery is described by the three-dimensional diameter corresponding to the maximum curvature, as shown in the Eq.(11).
In summary, H factor and d factor are used as two quantities to quantify the mechanical abuse conditions of the battery, as shown in Table 3.Moreover, battery SOC is used to quantify the battery's state.( 6)

Safety boundary analysis based on experimental data
In the battery mechanical abuse experiment, although the battery voltage can react in advance to ISC, the actual operation of the battery often involves charging and discharging cycles, causing continuous voltage fluctuations.Therefore, small voltage fluctuations cannot be used to determine the battery safety boundary.Choosing mechanical characteristic parameters during battery mechanical abuse is a more reasonable approach.
Considering that ISC slightly precedes the force peak, correction coefficients α F and α x are introduced, and in this experiment, α F = 0.84 and α x = 0.88 are calculated.
This paper conducts Pearson linear correlation coefficient analysis for input variables (SOC, H factor , d factor ) and output variables ( F cr and x cr ), as shown in Fig. 6.Generally, correlation strength is judged based on the following ranges, as shown in Table 4.The absolute value of the correlation indicates the correlation's strength; the closer the coefficient is to 1 or − 1, the stronger the correlation, while the closer it is to 0, the weaker the correlation.According to the correlation coefficient analysis table, it can be observed from Fig. 6 that F cr is strongly correlated with d factor , weakly correlated with H factor , and not correlated with SOC; x cr is strongly correlated with d factor , moderately correlated with H factor , and not correlated with SOC.
Therefore, based on the above analysis, linear correlation function models for F safe and x safe with H factor and d factor are constructed, and parameters are estimated through the least squares method to obtain Eqs. ( 13) and (14).Considering that the regression model is multivariate, the adjusted R 2 is used to describe the fitting degree of the model.The adjusted R 2 is very close to 1, indicating a high fitting accuracy of the function model.Figure 7a,b respectively show the surfaces of F safe and x safe , with black dots representing each experimental value and red dots representing the mean values of each abuse condition.( 12)  A significance test is conducted on the fitting parameters to validate the model and avoid overfitting.If the p-value is small, it indicates that the probability of the null hypothesis occurring is small, and if it occurs, according to the small probability principle, there is reason to reject the null hypothesis.In general, p > 0.05 indicates no significant difference; 0.01 < P < 0.05 indicates a significant difference; p < 0.01 indicates a highly    www.nature.com/scientificreports/significant difference.Table 5 shows the parameter values and corresponding p-values for the six model parameters, and the results indicate that all p-values are much less than 0.01.Therefore, the established linear regression model is highly reliable.Based on the above analysis, the safety boundary of battery mechanical abuse strongly linearly correlated with H factor and d factor is obtained.The safety force F safe is positively correlated with H factor and d factor , and the displacement boundary x safe is negatively correlated with H factor and positively correlated with d factor .The linear regression model established for the safety boundary allows for a convenient and efficient determination of the battery's safety boundary based on operating conditions, aiding practical engineering applications.

Safety boundary analysis based on finite element model
However, the above analysis only provides a representation of the safety boundary, and further explanation of its inherent correlation needs to be explained through mechanisms.In current research, the safety boundary of the battery can be described through failure criteria, commonly divided into Stress-based failure criteria and Strain-based failure criteria 44,45 .These criteria are usually analyzed by calculating the internal stress of the battery.When calculating the strain of the battery, it is necessary to know the magnitude of the force on the battery and the area of the force cross-section.In the experimental situation, the force on the battery can be obtained through the extrusion machine, but the force cross-sectional area is challenging to obtain in real time.Considering that the square battery's metal shell undergoes deformation similar to a beam structure under compression, making it challenging to obtain the force cross-sectional area through analytical methods, a finite element method is adopted to calculate the internal stress of the battery.
Figure 8a shows the finite element modeling schematic geometry, including the compression punch, battery shell, and two battery cores.Taking the 60 mm spherical punch as an example, Fig. 8b shows the schematic of the battery's deformation section with the punch's intrusion during the experiment.Zooming in on the contact surface between the battery and the punch, as shown in Fig. 8c, significant deformation occurs in the part of the battery shell that is not directly in contact with the punch after being pressurized.The finite element method can more conveniently simulate this scenario than analytical methods.
The battery shell and the punch are made of structural steel, and their modulus, density, and other parameters can be obtained by consulting literature.The battery core must undergo a modulus testing experiment to obtain its stress-strain curve.The stress-strain curve of the battery core was obtained from the flat plate extrusion experiment fitted using the isotropic model 46 .www.nature.com/scientificreports/where A and B are parameters obtained through experiments, σ p is plastic stress, ε p is plastic strain, and n is the hardening index.Reference 47 considers separator rupture when the internal stress of the battery reaches 43 MPa, which is the critical point for ISC in the battery.In this study, von Mises failure criteria σ e = 40MPa was adopted as the stress failure condition of the LF32 battery.The von Mises stress calculation is shown in the Eq. ( 16), where σ 1 , σ 2 , and σ 3 are the principal stresses of the material 48 .
Table 6 presents the parameters of the model.The model was simulated using COMSOL software to calculate the stress distribution of the battery under different mechanical abuses and the corresponding failure areas.The simulation boundary conditions were set: punch intrusion speed of 30 mm/min, intrusion distance combined with experimental results, and different punches corresponding to ISC displacement.
The simulation results of this study are shown in Fig. 9a-e, which plots the displacement and stress distribution of the battery in the corresponding experiments with 40 MPa as the stress upper bound.Comparing the simulation results of different battery groups, the larger the deformation, the higher the stress.Taking 40 MPa as the ISC boundary, the larger the compressed area of the battery, the larger the ISC area, as shown in Fig. 9f.Therefore, although the critical displacement and force for failure of the battery vary among different groups, the internal stress distribution pattern is relatively consistent and consistent with experimental analysis.(15)   www.nature.com/scientificreports/

Thermal runaway risk degree analysis
Upon exceeding the safety boundary, the battery will trigger the thermal runaway, leading to dangerous situations such as smoke and fire.The degree of thermal runaway risk is defined by calculating the total heat released during the entire thermal runaway process of the battery.Considering that the temperature difference of the battery has decreased after 200 s of the experiment, an analysis of the thermal images at 200 s is conducted.It is observed that, in addition to the temperature rise of the battery, the thermal runaway of the battery also causes a temperature increase in the punch and the steel block at the bottom of the battery.Thermal images of two typical experiments are shown in Supplementary Fig. S8 online.The convection heat dissipation with less influence within 200 s is ignored in the calculation.The enthalpy change during the experimental process is calculated using the Eq.(17)   where i = battery, punch, block represents the battery, punch, and bottom block; M i is the mass; Cp i is the specific heat capacity; T i is the average temperature at 200 s; and T i_0 is the initial temperature.Relevant parameters are shown in Table 7.
Figure 10 presents each condition's enthalpy change results for different SOC batteries.Within the same group, batteries with higher SOC release more energy during thermal runaway, and the enthalpy change increases with increasing SOC.Among different groups, the larger the compressed area of the battery, the higher the degree of ISC, resulting in a more significant heat release during ISC.The enthalpy change increases with the increase in the compressed area of the battery.This analysis result is consistent with the analysis result of the battery ISC in the electrical response in "Results and discussions".
To define the risk degree of the battery, an analysis of the battery's post-experimental state is needed to establish a baseline.The appearance of 20% SOC and 60% SOC batteries remains relatively intact except for the compressed area, while 80% SOC and 100% SOC batteries exhibit prominent burn areas outside the compressed region, as shown in Supplementary Fig. S9 online.
Batteries with SOC below 60% have a relatively small impact on the surroundings after thermal runaway.Therefore, conical 60% SOC is selected as the baseline, and normalization is applied.The thermal runaway risk degree Severty is defined and Severty is related to the experimental group and the battery SOC, as shown in Eq. (18).
A theoretical analysis of the thermal runaway during battery mechanical abuse is conducted to further analyze the relationship between the risk degree of batteries in the same group and different groups.Enthalpy change during mechanical abuse mainly includes heat generation from ISC ( Q isc ) and side reactions in the battery ( Q side ), as shown in the Eq. ( 19).www.nature.com/scientificreports/For Q side , experiments in literature 49-52 have conducted ARC thermal runaway experiments, and the Eq. (20)hows the relationship between the battery's highest temperature T max and Q side .Experimental data show that the highest temperature of the battery is proportional to the battery's SOC, as shown in Fig. 11a, and all R 2 values were above 0.954.
For Q isc , within the same group, the punch is the same, and the battery is damaged similarly, with similar voltage drop rates and degrees of ISC 35 , so Q isc is almost the same.For different groups, Q isc is calculated using the Eq. ( 21).V (t) , I isc (t) , and r isc (t) are difficult to obtain from experiments directly and usually require further combined accurate mechanical-electrical-thermal coupling models for simulation analysis 47,[53][54][55][56] .
Therefore, due to similar Q isc and Q side linearly correlated with SOC within the same group, combining Eqs. ( 18) and ( 19) a linear relationship between battery SOC and risk degree can be established, as shown in the Eq.(22).Q isc cannot be directly calculated for different groups, making quantitative analysis challenging.
Figure 11b shows the risk degree of batteries with different SOC in five experimental groups.The risk degree is strongly linearly related to the battery's SOC, the value of R 2 all above 0.936.In different groups, the risk degree of the battery increases with the increase in the area of the battery failure region but does not show a strong linear relationship.The Pearson correlation coefficients of Severty with d factor and H factor are 0.37 and 0.08, indicating a relatively low linear correlation degree.

Conclusions
The proposed experimental study provides a deep insight into battery thermal runaway behavior and safety assessment under mechanical abuse.The main conclusions are as follows:

Figure 1 .
Figure 1.The schematic of the mechanical abuse experiment.

Figure 2 .
Figure 2. The experiment results of mechanical abuse (sphere ɸ30 mm, 60 SOC).(a) Mechanical-electricalthermal response curve; (b) digital pictures and the infrared images of LFP cells during experiments.

Figure 4 .
Figure 4. Comparison of battery characteristic parameters under mechanical abuse.(a) Mechanical response characteristic parameters; (b) electrical response characteristic parameters; (c) thermal response characteristic parameters.

Figure 5 .
Figure 5. Three-dimensional geometry and mean curvature distribution of different punch.

Figure 8 .
Figure 8. Finite element modeling diagram.(a) Geometric diagram of extrusion process; (b) extrusion process battery and punch section; (c) enlarged diagram of battery force section.

Figure 10 .
Figure 10.Enthalpy change under different SOC with different punches.

1 .
Mechanical abuse experiments: Experiments under different punch shapes and state of charge (SOC) conditions revealed that the punch influences the pressure, voltage, and temperature of the battery during failure.Smaller punches result in lower pressures and displacements during battery failure, and a higher SOC results in a more severe thermal runaway.2. Feature parameter extraction: Key parameters such as maximum pressure, voltage drop rate, and highest temperature were extracted from battery response curves.3. Safety boundary analysis: H factor and d factor indices were introduced to quantify the mechanical abuse conditions, and a regression model for the battery's safety boundary was established with high accuracy.4. Thermal runaway risk assessment: The system enthalpy change during battery thermal runaway was analyzed, and a regression model for thermal runaway risk was proposed.The risk of thermal runaway in batteries was found to be correlated with SOC and the size of the failure area.

( 19 ) 5 Figure 11 .
Figure 11.(a) The relationship between SOC and thermal runaway maximum temperature in the literature; (b) the relationship between SOC and risk degree of different battery groups in the experiment.

Table 2 .
Experiment setup of abuse tests.

Table 3 .
Different punch quantized analysis parameters.

Table 4 .
Correlation coefficient analysis table.

Table 5 .
Model significance test: P-value calculation.

Table 6 .
Model parameter table.
a Experimental measurement results.bParameter fitting results.cReference from the software database.Figure 9. Critical state finite element simulation results.(a-e) Battery stress distribution in a critical state with different groups; (f) volume comparison of ISC region in different groups.

Table 7 .
Enthalpy change calculation related parameters table.
a Experimental data acquisition.b Calculation based on different punch shapes.